Tunable light source cavity detection using a plurality of axial-plus-transverse modes

ABSTRACT

Apparatuses, methods, and systems for detecting a substance are disclosed. One system includes a light source, an optical cavity, a cavity detector, and a processor. The light source generates a beam of electro-magnetic radiation, wherein a wavelength of the beam of electro-magnetic radiation is tuned to operate at multiple wavelengths. The optical cavity receives the beam of electro-magnetic radiation, wherein the physical characteristics of the cavity define a plurality of allowed axial-plus-transverse electro-magnetic radiation modes, wherein only a subset of the allowed axial-plus-transverse electro-magnetic radiation modes are excited when the optical cavity receives the beam of electro-magnetic radiation. The cavity detector senses electro-magnetic radiation emanating from the optical cavity. The processor operates to receive information relating to the sensed electro-magnetic radiation, and detects the substance within the optical cavity based on amplitude and/or phase of the sensed electro-magnetic radiation emanating from the optical cavity.

RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 15/909,909, filed Mar. 1, 2018, and claims priority to U.S.Provisional Patent Application Ser. No. 62/560,235 filed Sep. 19, 2017,all of which are herein incorporated by reference.

FIELD OF THE DESCRIBED EMBODIMENTS

The described embodiments relate generally to tunable light sourcesubstance detection. More particularly, the described embodiments relateto systems, methods and apparatuses for tunable light source cavitydetection using a plurality of axial-plus-transverse modes.

BACKGROUND

There are many applications and markets today where much effort is beinginvested to develop sensor technologies that have greater performance interms of sensitivity (parts per million or billion) and specificity(unambiguously detecting identified molecules) while offering theeconomics needed to deploy in a large scale to provide both qualitativeand quantitative data to improve safety, their infrastructure and tobetter the environment. One example of such a need is around natural gassensing (methane), a common energy source around the world. In theUnited States there are over 68 million homes and over 6 millionbuildings and thousands of factories that rely on natural gas. This gasis delivered via over 2.4 million miles of main gas pipelines havingdistributing pipes extending to homes/buildings and factories. This is acommon means of distributing energy in major cities around the world. Aswith any infrastructure, the pipes continue to age and are prone tohazardous leaks. Natural gas is a highly combustible odorless andcolorless hydrocarbon gas largely composed of methane. Gas leaks presenta serious safety and environment hazard and much effort has beeninvested in developing higher sensitivity and specificity sensors. Theneed to deploy sensors extending to residential homes and buildings hasplaced price/performance criteria on sensors that are not currentlysatisfied by existing technologies. The primary performance concernswith existing commercial sensors are that they do not have specificityand hence generate false positives to common household agents; level ofdetection is not sufficient and the range of sensing is limited.

The Oil and Gas industry also utilize a wide variety of gases thatpresent safety and environmental issues if not widely monitored forleaks. In the United State, Leak Detection And Repair (LDAR) programsare required as part of the Federal Regulations. A LDAR program is afacility's system of procedures used to locate and repair leakingcomponents (e.g., valves, pumps, connectors, compressors, and agitators)to minimize fugitive Volatile Organic Compounds (VOC) and Hazardous AirPollutants (HAP) emissions including but not limited to methane.

It is desirable to have methods apparatuses, and systems for tunablelight source cavity detection using a plurality of axial-plus-transversemodes.

SUMMARY

An embodiment includes a system for detecting a substance. The systemincludes a tunable light source, an optical cavity, a cavity detector,and a processor. The tunable light source generates a beam ofelectro-magnetic radiation, wherein a wavelength of the beam ofelectro-magnetic radiation is tuned to operate at a plurality ofwavelengths. The optical cavity receives the beam of electro-magneticradiation, wherein physical characteristics of the optical cavity definea plurality of allowed axial-plus-transverse electro-magnetic radiationmodes, wherein only a subset of the plurality of allowedaxial-plus-transverse electro-magnetic radiation modes are excited whenthe optical cavity receives the beam of electro-magnetic radiation. Thecavity detector senses electro-magnetic radiation emanating from theoptical cavity. The processor operates to receive information relatingto the sensed electro-magnetic radiation, and detect the substancewithin the optical cavity based on at least one of an intensity, anamplitude, a phase, or an amplitude and phase of the sensedelectro-magnetic radiation emanating from the optical cavity at one ormore of the plurality of wavelengths while the optical cavity receivesthe beam of electro-magnetic radiation.

Another embodiment includes a method of detecting a substance. Themethod includes generating, by a tunable light source, a beam ofelectro-magnetic radiation, wherein a wavelength of the beam ofelectro-magnetic radiation is tuned to operate at a plurality ofwavelengths, receiving, by an optical cavity, the beam ofelectro-magnetic radiation, wherein physical characteristics of theoptical cavity define a plurality of allowed axial-plus-transverseelectro-magnetic radiation modes, wherein only a subset of the pluralityof allowed axial-plus-transverse electro-magnetic radiation modes areexcited when the optical cavity receives the beam of electro-magneticradiation, sensing, by a cavity detector, electro-magnetic radiationemanating from the optical cavity, receiving, by a processor,information relating to the sensed electro-magnetic radiation, anddetecting the substance within the optical cavity based on at least oneof an intensity, an amplitude, a phase, or an amplitude and phase of thesensed electro-magnetic radiation emanating from the optical cavity atone or more of the plurality of wavelengths while the optical cavityreceives the beam of electro-magnetic radiation.

Other aspects and advantages of the described embodiments will becomeapparent from the following detailed description, taken in conjunctionwith the accompanying drawings, illustrating by way of example theprinciples of the described embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system for detecting a substance,according to an embodiment.

FIG. 2 is a block diagram that includes misalignment of the incomingbeam to an axis of the optical cavity.

FIG. 3 is a block diagram that includes more detail of a system fordetecting a substance, according to an embodiment.

FIG. 4 is a block diagram that includes mode matching a beam ofelectro-magnetic radiation to an optical cavity, wherein a waist sizeand a waist location beam of electro-magnetic radiation matches a waistsize and waist location defined by a physical design of the opticalcavity.

FIG. 5 shows examples of Hermite-Gaussian transverse modes, according toan embodiment.

FIG. 6 shows an example of a triangle waveform being used to tune awavelength of the laser, according to an embodiment.

FIG. 7 shows an example of discrete steps being used to change thewavelength of the laser, according to an embodiment.

FIG. 8 shows an example of summing areas under eachaxial-plus-transverse mode, according to an embodiment.

FIG. 9 shows a plot that depicts an example of axial modes, eachcontaining multiple transverse modes, according to an embodiment.

FIG. 10 shows a plot and a table that depict an example of summing peakamplitude measurements of axial-plus-transverse modes made with acavity-detector, according to an embodiment.

FIG. 11 shows an example of a block diagram that includes a referencesubstance and beam normalization, according to an embodiment.

FIG. 12 shows a calculated intensity as sensed by a normalizationdetector, according to an embodiment.

FIG. 13 shows an absorbance spectra for methane when measured atatmospheric pressure, according to an embodiment.

FIG. 14 shows an example of a reference cell detector signal when theaverage laser ramp voltage corresponds to the peak wavelength of thereference absorbance feature, according to an embodiment.

FIG. 15 is a flow chart that includes steps of a method to measure data,according to an embodiment.

DETAILED DESCRIPTION

The embodiments described include methods, apparatuses, and systems fortunable light source cavity detection using a plurality of allowedaxial-plus-transverse modes.

FIG. 1 is a block diagram of a system for detecting a substance,according to an embodiment. The system includes a tunable light source110, an optical cavity 120, a cavity detector 130, and a processor 140.For an embodiment, the tunable light source 110 generates a beam ofelectro-magnetic radiation, wherein a wavelength of the beam ofelectro-magnetic radiation is tuned to operate at a plurality ofwavelengths. The optical cavity 120 receives the beam ofelectro-magnetic radiation, wherein physical characteristics of theoptical cavity 120 define a plurality of allowed axial-plus-transverseelectro-magnetic radiation modes, wherein only a subset of the pluralityof allowed axial-plus-transverse electro-magnetic radiation modes areexcited when the optical cavity 120 receives the beam ofelectro-magnetic radiation. The cavity detector 130 senseselectro-magnetic radiation emanating from the optical cavity 120. Theprocessor 140 operates to receive information relating to the sensedelectro-magnetic radiation, and detect the substance within the opticalcavity 120 based on at least one of an intensity, an amplitude, a phase,or an amplitude and phase of the sensed electro-magnetic radiationemanating from the optical cavity 120 at one or more of the plurality ofwavelengths while the optical cavity 120 receives the beam ofelectro-magnetic radiation.

FIG. 2 is a block diagram that includes misalignment of the incomingbeam (of the tunable light source 110) to an axis 224 of an opticalcavity 220. For at least some embodiments, the subset of the pluralityof the allowed axial-plus-transverse electro-magnetic radiation modes isexcited by misaligning the incoming beam of electro-magnetic radiationwith the axis 224 of the optical cavity 220. For an embodiment, thesubset includes a number greater than one. The optical cavity 220includes cavity mirrors 223, 222. A cavity detector 230 senseselectro-magnetic radiation emanating from the optical cavity 220.

For at least some embodiments, the subset of the plurality of theallowed axial-plus-transverse electro-magnetic radiation modes isexcited by mode mismatching a waist size and/or a waist location of theincoming beam of electro-magnetic radiation to the allowedaxial-plus-transverse modes that are defined by the optical cavity. Foran embodiment, the incoming beam of electro-magnetic radiation comprisesmore than one transverse mode. For at least some embodiments, the beamof electro-magnetic radiation in the cavity impacts one location on eachmirror that defines the cavity.

A first implementation could include cavity-based implementations thatutilize the amplitude of a single axial-plus-transverse electro-magneticradiation mode of the cavity which is enhanced using a single wavelengthlaser. Further, the absorption of one axial-plus-transverseelectro-magnetic radiation mode is quantified, when the singlewavelength laser is no longer enhancing (the laser diode is turned offand/or not transmitting electro-magnetic radiation) theaxial-plus-transverse electro-magnetic radiation mode of the cavity. Asecond implementation could utilize a single wavelength laser so thatthe interaction between the laser and the cavity always excites theentire plurality of allowed axial-plus-transverse electro-magneticradiation mode defined by the cavity. However, both of theseimplementations require very precise cavity alignment and very expensiveoptical components. In contrast, the described embodiments do notrequire precise cavity alignment and can be configured with low-costoptical components.

As shown, the embodiment of FIG. 1, a tunable light source cavitydetection system utilizing multiple wavelengths, using a subset of theplurality of allowed axial-plus-transverse electro-magnetic radiationmodes of the cavity, whereby summing the information from a subset ofthe plurality of allowed axial-plus-transverse electro-magneticradiation modes while the tunable light source enhances theaxial-plus-transverse electro-magnetic radiation modes of the cavity,enables the use of low cost optical components.

FIG. 3 is a block diagram that includes more detail of a system fordetecting a substance, according to an embodiment. For this embodiment,the tunable light source 110 is implemented with a tunable laser 210.For this embodiment, a free space beam of electro-magnetic radiation,emitted by the continuous wave, wavelength-tunable laser 210 impactslens 1 (251) which collimates the beam of electro-magnetic radiation.The collimated beam of electro-magnetic radiation travels to a firstfiber collimator (FiberPort) 256. The beam of electro-magnetic radiationthen passes through a fiber isolator 255. The beam of electro-magneticradiation then passes through a second fiber collimator (FiberPort) 257that transforms the beam of electro-magnetic radiation, once again intoa free-space beam of electro-magnetic radiation.

For at least some embodiments, the fiber isolator 255 serves twopurposes, (1) to help suppress all but the desired mode or modes (TEMOOTransverse Electro-magnetic Mode, and (2) to isolate the laser sourcefrom back reflections that might be generated from optical components.

For at least some embodiments, the free-space beam of electro-magneticradiation emitted from the second fiber collimator (FiberPort) 257 thenimpacts lens #2 (252) and lens #3 (253) and passes through beam steeringmirrors 254.

As shown in FIG. 2, for an embodiment, the optical cavity 220 includes acavity entrance mirror 223 and two cavity mirrors 221, 222. Afterpassing through the beam steering mirrors 254, the electro-magneticradiation then enters the three mirror optical cavity 220 through thepartially reflecting optical cavity entrance mirror 223. As shown, theoptical cavity 220 includes an arrangement of mirrors 221, 222, 223 thatforms a standing wave cavity. For an embodiment the optical cavity canbe configured as a traveling wave cavity.

FIG. 4 is a block diagram that includes mode matching a beam ofelectro-magnetic radiation to an optical cavity, wherein a waist sizeand a waist location of the beam of electro-magnetic radiation matches awaist size and waist location defined by a physical design of theoptical cavity. While the cavity design of FIG. 4 includes only twomirrors (mirrorl, mirror2), the descriptions are applicable to the threemirror cavity of FIG. 3. The incoming beam of electro-magnetic radiationis considered mode matched to the optical cavity 220 when the incomingbeam of electro-magnetic radiation's waist size and waist locationmatches that defined by the physical design of the optical cavity 220.The waist size 290 of electro-magnetic radiation is defined as thephysical size of the electro-magnetic field pattern of radiationmeasured in a reference plane perpendicular (i.e., transverse) to thepropagation direction of the electro-magnetic radiation. The waistlocation 280 of electro-magnetic radiation is defined as the physicallocation of the waist. When the waist size 290 or waist location 280 ofthe incoming beam of electro-magnetic radiation, is not mode matched bythat defined by the optical cavity, a subset of the plurality of allowedaxial-plus-transverse electro-magnetic radiation modes in the cavitywhich is greater than one can be excited.

The incoming beam of electro-magnetic radiation is considered alignedwith the cavity when the incoming beam is steered into the opticalcavity 220 such that the incoming beam of electro-magnetic radiation iscongruent with the optical cavity axis. When the incoming beam ofelectro-magnetic radiation differs (not congruent or misaligned) withthe cavity axis, a subset of the plurality of allowedaxial-plus-transverse electromagnetic radiation modes in the cavitywhich is greater than one can be excited.

For an embodiment, the incoming beam of electro-magnetic radiationincludes one or more transverse modes. When the incoming beam ofelectro-magnetic radiation includes more than one transverse mode, asubset of the plurality of allowed axial-plus-transverse electromagneticradiation modes in the cavity which is greater than one can be excited.

Referring back to FIG. 3, for at least some embodiments, the lens #2(252) and lens #3 (254) act as a telescope that matches the waist sizeand waist location of the incoming beam to that defined by the design ofthe optical cavity 220. For at least some embodiments, by changing theposition of lens #2 and lens #3 along the direction of theelectro-magnetic radiation, the waist size and/or waist location can bemode mismatched to that defined by the cavity.

In an embodiment, the incoming beam of electro-magnetic radiationincludes one transverse mode. The beam is aligned with the optical axisof the cavity. A waist size and/or waist location of the incoming beamof electro-magnetic radiation is selected to be a different (not modematched) from that defined by the physical design of the optical cavity220 thereby exciting a subset of the plurality of allowedaxial-plus-transverse electro-magnetic radiation modes in the cavitywhich is greater than one.

In an embodiment, the incoming beam of electro-magnetic radiation isdescribed as one transverse electro-magnetic mode, a waist size and/orwaist location of the incoming beam of electromagnetic radiation isselected to be the same as that defined by the physical design of theoptical cavity 220. The beam is steered into the optical cavity 220 sothat the incoming beam of electro-magnetic radiation is misaligned withthe optical cavity axis thereby exciting a subset, which is greater thanone, of the plurality of the allowed axial-plus-transverseelectro-magnetic radiation modes. In an embodiment, this misalignment isimplemented using two beam steering mirrors 254 to steer theelectro-magnetic radiation into the optical cavity 220 such that amisalignment is created by introducing a displacement between theincoming beam of electro-magnetic radiation and the optical cavity axisof the optical cavity 220 thereby resulting in a beam ofelectro-magnetic radiation within the optical cavity 220 that excitesonly a subset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes which is greater than one. One methodto displace the incoming beam of electro-magnetic radiation is to usethe two steering mirrors 254 to tilt the incoming beam ofelectro-magnetic radiation so that it is misaligned with the opticalcavity axis thereby exciting a subset, which is greater than one, of theplurality of the allowed axial-plus-transverse electro-magneticradiation modes.

In another embodiment, the incoming beam of electro-magnetic radiationincludes more than one transverse mode(s), thereby exciting a subset ofthe plurality of allowed axial-plus-transverse electro-magneticradiation modes in the cavity which is greater than one.

In another embodiment, the incoming beam of electro-magnetic radiationincludes more than one transverse mode(s). The incoming beam ofelectro-magnetic radiation is aligned with the cavity axis. A waist sizeand/or waist location of the incoming beam of electro-magnetic radiationis selected to be a different size than that defined by the physicaldesign of the optical cavity 220 thereby exciting a subset of theplurality of allowed axial-plus-transverse electro-magnetic radiationmodes in the cavity which is greater than one.

In another embodiment, the incoming beam of electro-magnetic radiationcomprises more than one transverse mode. A waist size and/or waistlocation of the incoming beam of electromagnetic radiation is selectedto be the same as that defined by the physical design of the opticalcavity 220. The incoming beam of electro-magnetic radiation ismisaligned with the optical axis of the cavity, thereby exciting asubset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes in the cavity which is greater than one

In addition to the previously mentioned embodiments utilizing a singletunable light source to generate more than one transverse mode in thecavity, there are at least two other methods to generate more than onetransverse modes in the cavity. One embodiment includes a light sourcethat generates multiple transverse modes, and another embodimentincludes using multiple light sources.

For at least some embodiments, the cavity detector 230 is placed suchthat the cavity detector 230 senses electro-magnetic radiation emanatingfrom the optical cavity 220. The cavity detector 230 receiveselectro-magnetic radiation exiting the optical cavity 220 and produces avoltage or current that is proportional to the electro-magneticradiation sensed by the cavity detector 230. The electro-magneticradiation sensed by the cavity detector 230 is representative of theelectro-magnetic radiation intensity inside the optical cavity 220, andfor at least some embodiments, it is this electro-magnetic radiationthat represents the electro-magnetic intensity, amplitude, a phase, oran amplitude and phase at a plurality of wavelengths.

For at least some embodiment, the cavity detector 230 generates data(sensed) in an analog form. For at least some embodiments, for inputinto and processing by the processor 240, the analog data is convertedinto digital form by and ADC (analog to digital converter) 291. Theprocessor 240 records the received output at the plurality ofwavelengths and detects the substance. For an embodiment the substanceis detected based on the intensity, amplitude, a phase, or an amplitudeand phase of the sensed electro-magnetic radiation emanating from theoptical cavity 220 at one or more of the plurality of wavelengths whilethe optical cavity 220 receives the beam of electro-magnetic radiation.

For at least some embodiments, the incoming beam of electro-magneticradiation can be described or represented by a linear combination oftransverse modes. The transverse mode of electro-magnetic radiation isdefined as a particular (transverse) electro-magnetic field pattern ofradiation measured in a plane perpendicular (i.e., transverse) to thepropagation direction of the electro-magnetic radiation. If a transversewave is moving in the z direction, its oscillations lie in the x-yplane, and the Electric field oscillates in one plane, for instance thex plane, while the Magnetic field oscillates in the perpendicular plane,for instance the y plane.

FIG. 5 shows examples of Hermite-Gaussian transverse modes, according toan embodiment. Specifically, FIG. 5 shows examples of transverse modesfor a beam of light, such as the light generated by a laser. The darkareas represent the concentration of intensity in the cross sectionslice of the wave propagating in the medium (free space or opticalcavity) on the z-plane.

The term ũ₀(x,z)ũ_(o(y,z)) is referred to as the lowest-order Gaussianmode (TEM 00) and its transverse component can be described as a round“slab” or disk. The function ũ₁(x,z)ũ₀(y,z) is called the first-orderGaussian mode in x and the lowest-order mode in y and as can be seen inFIG. 5 has two lobes along the x dimension. The function ũ₀(x,z)ũ₁(y,z)is called the first-order Gaussian mode in y and the lowest-order modein x and as can be seen in FIG. 5 the beam has two lobs alone the ydimension. For higher order modes, the same logic can be used. TheseGaussian modes can, under specific conditions, be used to describe abeam of electro-magnetic radiation travelling in free-space or in aoptical cavity

A beam of Electro-magnetic radiation in an optical cavity (such as,optical cavity 220) can also be described using axial—plus-transversemodes that are allowed. Allowed cavity modes (allowedaxial-plus-transverse electro-magnetic radiation modes) can beunderstood using a framework in the wavelength domain.

When resonator theory is applied to an arrangement of 2 or more mirrorsforming an optical cavity, the steady-state resonance condition becomes,

${r_{1}r_{2}r_{3}\mspace{14mu} \ldots \mspace{14mu} r_{n}e^{{- j}\frac{\omega \rho}{c}}} = 1$

where the coefficients r₁, r₂, r₃, . . . r_(n) are the wave-amplitudereflection coefficients for mirror 1, mirror 2, mirror 3, ... mirror nwhich defines the cavity; ω is the angular frequency of the opticalwave, λ is the wavelength of the optical wave, c is the speed ofelectro-magnetic radiation,

${e^{- j}\frac{\omega\rho}{c}} = 1$

is the phase shift for one full trip around the optical cavity with around—trip distance designated as p, and ψ_(nm) is the “Guoy phaseshift” phase angle. The resonance condition equation expresses theround-trip phase shift conditions under which the system oscillates withgreater electro-magnetic amplitudes than when the resonance condition isnot met. The greater amplitudes produced while meeting this resonancecondition is called allowed axial-plus-transverse modes. FIG. 5 shows anexample of allowed axial-plus-transverse modes. The “allowed”axial-plus-transverse modes in the optical cavity are those where thecavity round-trip distance is equal to an integer number of wavelengths

Allowed axial-plus-transverse modes can occur at a plurality ofwavelengths. Axial-plus-transverse modes in an optical cavity can bedescribed mathematically in the following manor. The electro-magneticamplitude in an optical cavity can be described in Cartesian coordinatesusing the paraxial wave equation:

${( {\frac{\partial^{2}}{\partial x^{2}} + {{\frac{\partial^{2}}{\partial y^{2}}{+ 2}}jk\frac{\partial}{\partial z}}} ){\overset{\sim}{E}( {x,y,z} )}} = 0$

where {tilde over (E)}(x, y, z)=0 is the electro-magnetic amplitude inthe cavity.

The “Guoy phase shift” is associated with the fact that differentaxial-plus-transverse modes can accumulate phase at different rates. Ifone identifies the axial-plus-transverse modes of a given opticalcavity, one can also find the exact angular frequencies (wavelengths) atwhich the resonance condition is met. The resonance angular frequencies,including the Guoy phase shift, of the Hermite-Gaussianaxial-plus-transverse modes for a two mirror cavity made up of mirrorsM₁ and M₂ are given by a plurality of wavelengths described by:

$\omega = {\omega_{qnm} = {\lbrack {q + {( {n + m + 1} )\frac{\cos^{- 1} \pm \sqrt{g_{1}g_{2}}}{\pi}}} \rbrack \times \frac{2\pi \; c}{p}}}$

where p is the round-trip path length in the optical cavity, c is thespeed of electro-magnetic radiation, and where the parameters “g” aregiven by;

$g_{1} \equiv {1 - {\frac{L}{R_{1}}\mspace{14mu} g_{2}}} \equiv {1 - \frac{L}{R_{2}}}$

where the parameters R₁ and R₂ are the radius of curvatures of mirror M₁and M₂, respectively. The resonance angular frequencies are degeneratewith respect to the indices n and m through the (n+m+1) term

In cylindrical coordinates, the resonance angular frequencies of theLaguerre-Gaussian axial-plus-transverse modes in the optical cavity arethen given by a plurality of wavelengths described by,

$\omega = {\omega_{qpl} = {\lbrack {q + {( {{l} + {2p} + 1} )\frac{\cos^{- 1}( {\pm \sqrt{g_{1}g_{2}}} )}{\pi}}} \rbrack \times ( \frac{2\pi \; c}{p} )}}$

In this case, the resonance angular frequencies are degenerate withrespect to the indices l and p through the (|l|+2p+1) term.

In an embodiment, electro-magnetic amplitudes at a plurality ofwavelengths can be excited using two beam steering mirrors to create amode mismatch between the incoming beam of electro-magnetic radiationand the optical cavity. The number of allowed axial-plus-transverseelectro-magnetic radiation modes excited is related to the amount ofmisalignment between the incoming beam of electro-magnetic radiation andthe optical cavity axis. The electro-magnetic amplitude of theaxial-plus-transverse modes is related to the amount of misalignmentbetween the incoming beam of electro-magnetic radiation and the opticalcavity axis.

In mathematical terms, in the case where the optical cavity has losses,the angular frequencies, which make up optical cavity modes cannot becompletely described as delta functions. With optical loss, theelectro-magnetic radiation in the optical cavity can be described as asuperposition of a large number of waves, separated by equal phaseshifts but with amplitudes that are geometrically reduced by loss in theoptical cavity. Because of this geometric term, the higher the opticalcavity loss translates to a wider axial-plus-transverse cavity mode inthe frequency domain. When considering a plurality ofaxial-plus-transverse modes, overlapping frequencies of two or moremodes can cause transverse mode beating which will introduce largeintensity variations, as a function of time, in each undistinguishedaxial-plus-transverse mode. This inter-modulation distortion will resultin a noisier measurement thereby degrading system signal-to-noise ratioand sensitivity. As an example, suppose an optical cavity is oscillatingsimultaneously in two indistinguishable modes in the frequency domain.The indices of these modes is q₁n₁m₁ and q₂n₂m₂. The total output powerfrom the cavity associated with these two indistinguishable modes can bewritten as;

i(t)=I ₀₁ +I ₀₂ +I ₁₂ cos[(ω₂−ω1)t+ϕ ₁₂]

where I₀₁ and I₀₂ are the dc intensities due to each separate mode, plusa cross product or beat frequency term I₁₂ cos[(ω₂−ω₁)t+ϕ₁₂] between thetwo signals. If both modes have the exact same frequency, as in thedegenerative case, then (ω₂−ω₁)=0 and there is no time dependence oni(t). However, if (ω₂−ω₁)≠0, then there will be a time dependentvariation of the total intensity, i (t) with a period defined by thefrequency separation of the two modes. This time dependent variationwould introduce unwanted noise on the intensity measurement therebyimpacting performance. The axial-plus-transverse modes excited is asubset of the allowed axial-plus-transverse optical cavity modes that,except in the degenerative case, do not overlap in the frequency domainand/or do not produce mode beating (mixing products) and/or minimizemode beating in the frequency domain.

Laser Tuning

As previously described, for an embodiment, the laser generates a beamof electro-magnetic radiation, wherein a wavelength of the beam ofelectro-magnetic radiation is tuned to operate at a plurality ofwavelengths. For at least some embodiments, each axial-plus-transverseoptical cavity mode is excited when electro-magnetic radiation enteringthe optical cavity 220 meets the resonance conditions of the opticalcavity, including excitation wavelength.

At least some embodiments include continuous Laser Current and/orTemperature Tuning. Specifically, in an embodiment, the laser currentand/or laser temperature is varied over a range of currents and/ortemperatures thus causing the laser to radiate electro-magnetic energyover a range of different wavelengths (frequencies). For an embodiment,these variations in current and/or temperature are periodic and can bedescribed using linear (such as a triangle wave in FIG. 6), sinusoidalor non-sinusoidal waveforms; resulting in variations in the laserwavelength. By varying the wavelength, a plurality ofaxial-plus-transverse electro-magnetic radiation modes is excited. FIG.6 shows an example of a triangle waveform being used to tune awavelength of the laser, according to an embodiment. That is, FIG. 6shows an example of greater and lesser electro-magnetic intensities at aplurality of wavelengths while varying the laser wavelength using atriangle waveform.

At least some embodiments include discrete laser current tuning.Specifically, in an embodiment, the laser current is varied using asequence of current steps. These discrete steps in current result indiscrete steps in the laser wavelength. By stepping the laserwavelength, a plurality of axial-plus-transverse electro-magneticradiation modes is activated. FIG. 7 shows an example of discrete stepsbeing used to change the wavelength of the laser, according to anembodiment. Specifically, FIG. 7 shows an example of greater and lesserelectro-magnetic intensities while varying the laser wavelength usingdiscrete steps.

For at least some embodiments, detecting the substance is based on avariation in a shape of an intensity, an amplitude, a phase, or anamplitude and phase of axial-plus-transverse electro-magnetic modes ofthe sensed electro-magnetic radiation. When optical loss is introduced,axial-plus-transverse electro-magnetic radiation modes no longerresonate at a single frequency. FIG. 8 shows an example of summing areasunder each axial-plus-transverse mode, according to an embodiment.Specifically, FIG. 8 shows each axial-plus-transverse electro-magneticradiation mode has intensity variation in the frequency domain. In anembodiment, integrating over the excited intensity at a plurality ofwavelengths provides information about optical cavity loss.

Hermite-Gaussian modes can be used to describe the electro-magneticamplitudes in the cavity. FIG. 9 shows a plot 910 that depict an exampleof axial modes, each containing multiple transverse modes, according toan embodiment. Specifically, the plot 910 of FIG. 9 shows an example ofa plurality of Hermite-Gaussian axial-plus-transverse electro-magneticradiation modes. In this example, three sets of axial modes, q, eachcontaining multiple transverse modes, have been excited. Each mode isdesignated as TEM., where the integer n is the x-coordinate index andthe integer m is the y-coordinate index. By comparing intensities at theplurality of wavelengths with theory, axial-plus-transverseelectro-magnetic radiation modes can be identified and the peakintensity for each can be determined.

In an embodiment, the laser wavelength is varied to activate a pluralityof allowed axial-plus-transverse electro-magnetic radiation modes and atleast one of an intensity, an amplitude, a phase, or an amplitude andphase of the sensed electro-magnetic radiation emanating from theoptical cavity are detected. The repetitive pattern can be used touniquely identify each mode and associate the measured electro-magneticradiation to each axial-plus-transverse mode.

In another embodiment, the laser wavelength is varied to activate aplurality of allowed axial-plus-transverse electro-magnetic radiationmodes and at least one of an intensity, an amplitude, a phase, or anamplitude and phase of the sensed electro-magnetic radiation emanatingfrom the optical cavity are detected. The amplitude of the laser tuningvoltage can be used to uniquely identify each mode and associate themeasured electro-magnetic radiation to each axial-plus-transverseoptical cavity mode.

For at least some embodiments, detecting the substance includes summingat least one of an intensity, an amplitude, a phase, or an amplitude andphase of allowed axial-plus-transverse electro-magnetic modes of thesensed electro-magnetic radiation. Because the electro-magneticradiation in an optical cavity is governed by optical losses and whereinthe cavity detector senses electro-magnetic radiation emanating from theoptical cavity, the cavity detector can provide a measurement of opticalloss in the cavity. at least one of an intensity, an amplitude, a phase,or an amplitude and phase of each excited axial-plus-transverseelectro-magnetic radiation mode can be measured. For example, by summingthe peaks intensities of identified axial-plus-transverse optical cavitymodes over a plurality of wavelengths, information about optical cavityloss can be obtained. FIG. 10 shows a plot 1010 and a table 1020 thatdepict an example of summing peak amplitude measurements ofaxial-plus-transverse modes made with a cavity-detector, according to anembodiment. For at least some embodiments, the summation includes one ormore of the measured excited allowed axial-plus-transverse opticalcavity modes.

At least some embodiments further include a second normalizationdetector (such as, normalization detector 261) sensing electro-magneticradiation reflected off an entrance to the optical cavity, wherein theprocessor further operates to monitor the sensed electro-magneticradiation reflected off the entrance to the optical cavity. In order torepresent the electro-magnetic radiation intensity entering the opticalcavity, the beam reflected from the entrance to the optical cavity canbe monitored. FIG. 11 shows an example of a block diagram that includesa reference substance detector 263 and normalization detector 261,according to an embodiment. In this embodiment, electro-magneticradiation from the laser (beam from cavity injection system) is directedinto the optical cavity 220. A portion of that electro-magneticradiation passes through the partially reflecting cavity entrance mirror223 while another portion is reflected off the cavity entrance mirror223. The electro-magnetic radiation reflected off the cavity entrancemirror 223 is transported to the partially reflecting beam splitter 260.At the beam splitter 260 a portion of the electro-magnetic radiation istransmitted through the beam splitter 260 and sensed by the photodetector, such as, the normalization detector 261. A beam normalizationmeasurement of the normalization detector 261 must be made atwavelengths where the optical cavity 220 is not in resonance. When theoptical cavity 220 is not in resonance, the electro-magnetic radiationsensed by the normalization detector 261 is proportional to theelectro-magnetic radiation entering the optical cavity 220.

For at least some embodiments, the processor 240 further operates toaccount for effects of electro-magnetic radiation changes emanating fromthe optical cavity 220 caused by changes in an intensity, amplitude,phase, or amplitude and phase of the electro-magnetic radiation enteringthe optical cavity 220 including measuring the intensity, amplitude,phase, or amplitude and phase of the sensed electro-magnetic radiationreflected off the entrance to the optical cavity 220 and correcting theelectro-magnetic radiation emanating from the cavity based on theintensity, amplitude, phase, or amplitude and phase measured by thenormalization detector 261.

FIG. 12 shows a calculation of the intensity as sensed by thenormalization detector 261, according to an embodiment. Specifically, inthis embodiment the electro-magnetic radiation reflected off the opticalcavity entrance mirror is monitored using the normalization detector 261while varying the laser wavelength. As the laser frequency is alteredthe optical cavity goes into and out of optical cavity resonancesrepeating the pattern for each free-spectral range of the opticalcavity. When off resonance, the intensity of the electro-magneticradiation on the normalization detector 261 is proportional to the beamintensity entering the cavity and as such is a monitor signal for thelight intensity entering the optical cavity 220.

In an embodiment, by comparing the output of the cavity detector withthe output of the normalization detector 261, corrections forelectro-magnetic radiation changes emanating from the optical cavity 220caused by changes in the intensity of the electro-magnetic radiationentering the optical cavity 220 can be made.

For at least some embodiments, the processor further operates to tunethe wavelength of the beam of electro-magnetic radiation based onmonitoring electro-magnetic radiation exiting from a referencesubstance, wherein at least a portion of the electro-magnetic radiationreflected off the entrance to the optical cavity is passed through thereference substance, and wherein the reference substance is selected toinsure that a frequency of the electro-magnetic radiation corresponds toa frequency at which an absorption of the substance is measured.

In an embodiment, the beam of electro-magnetic radiation from the laserenters the optical cavity 220 through the partially reflecting opticalcavity entrance mirror 223. A portion of that electro-magnetic radiationpasses through the partially reflecting optical cavity entrance mirror223 while another portion is reflected off the mirror 223. Theelectro-magnetic radiation reflected off the cavity entrance mirror 223is transported to the partially reflecting beam splitter 260. At thisbeam splitter 260 a portion of the electro-magnetic radiation isreflected off the beam splitter 260 and is directed through thereference substance 262 and sensed by the reference substance detector263 as shown in FIGS. 3 and 11.

For an embodiment, the reference substance has enough reference speciesof interest to make an absorption measurement possible, and must havesufficient path length to make an absorption measurement.

The processor 240 receives the information of the sensedelectro-magnetic radiation from the Reference Substance detector 263 andfurther operates to tune the wavelength of the beam of electro-magneticradiation by adjusting the laser ramp offset voltage such that theaverage laser ramp voltage corresponds to a wavelength consistence withthe absorbance wavelength of the substance of interest. This ensuresthat the laser remains centered at the wavelength of the absorbancefeature and as such centered on the absorbance of the substance ofinterest. FIG. 23 shows an absorbance spectra for methane when measuredat atmospheric pressure, according to an embodiment.

For at least some embodiments, as in the case of a normalizationdetermination, a valid reference substance determination requires thatthe measurement be made when the optical cavity 220 is not in resonance.For an embodiment, this requirement is, again, met by selecting laserfrequencies where the optical cavity is not in resonances. For anembodiment, this is accomplished by monitoring the signal on the cavitydetector 230 and selecting laser frequencies where no optical cavityresonances occur.

FIG. 14 shows an example of a reference cell detector signal when theaverage laser ramp voltage corresponds to the peak wavelength of thereference absorbance feature, according to an embodiment. Specifically,the calculated reference substance detector signal when the averagelaser ramp voltage corresponds to the peak wavelength of the methaneabsorbance feature is shown in FIG. 14.

For at least some embodiments, the processor further operates to tunethe beam of electro-magnetic radiation over the plurality of wavelengthsone or multiple times, and record the information related to the sensedelectro-magnetic radiation at the plurality of wavelengths. For at leastsome embodiments, the processor further operates to sum the recordedinformation related to the sensed electro-magnetic radiation for each ofthe plurality of wavelengths over the one or multiple times. For atleast some embodiments, the processor further operates to identifyrepetitive patterns in the recorded information related to the sensedelectro-magnetic radiation for each of the plurality of wavelengths overthe one or multiple times. For at least some embodiments, the processorfurther operates to detect an amount of the substance based on theidentified repetitive patterns in the summed recorded informationrelated to the sensed electro-magnetic radiation for each of theplurality of wavelengths over the one or multiple times.

More information regarding the optical loss can be obtained by tuningthe laser to the same plurality of wavelengths multiple times. FIGS. 6and 7 depict laser control system signals in which the processor 240operates to repeatedly tune the beam of electro-magnetic radiation overthe same plurality of wavelengths multiple times. For an embodiment, theprocessor 240 further operates to record intensity of the receivedoutput at the plurality of wavelengths at each of the plurality ofwavelengths, each of the multiple times. For an embodiment, theprocessor 240 further operates to sum the recorded intensity for each ofthe plurality of wavelengths over the multiple times. For an embodiment,the processor further operates to identify repetitive patterns in thesummed recorded intensity for each of the plurality of wavelengths overthe multiple times. For an embodiment, the processor further operates todetect the amount of the substance based on the identified patterns inthe summed recorded intensity for each of the plurality of wavelengthsover the multiple times.

For an embodiment, the cavity includes an optical cavity 220 wherein theoptical cavity 220 comprises 2 or more mirrors forming the opticalcavity, wherein the optical cavity receives the beam of electro-magneticradiation; wherein successive reflections of the electro-magneticradiation at each of the 2 or more mirrors occurs at one common physicallocation on each mirror.

For an embodiment, the beam of electro-magnetic radiation is selected toensure that one axial-plus-transverse electro-magnetic mode is dominateat any one of the plurality of wavelengths.

For at least some embodiments, the processor receives information fromone or more detectors relating to a portion of the beam ofelectro-magnetic radiation not entering the cavity, wherein thedetectors (261, 263) are arranged in a physical configuration such thatthe information they provide in conjunction with the sensed (sensed bycavity detector 260) electro-magnetic radiation emanating from theoptical cavity increases the measurement range of the substancedetectable, wherein the sensed signal in conjunction with the cavitydetector increases the measurement range of the substance detectable.Specifically, information received from the cavity detector andinformation received from one or more detectors is used to detect thesub stance.

For an embodiment, the amount of the substance detected is limited bythe cavity detector and processor's capability to measure excitedallowed axial-plus-transverse electro-magnetic radiation modes when themajority of electro-magnetic radiation in the cavity is absorbed by thesubstance. Information from one or more detectors sensingelectro-magnetic radiation not entering the cavity may be used to detectthe substance when a substance absorbs the majority of electro-magneticradiation in the cavity. Combining the information from the cavitydetector and the information from one or more detectors sensingelectro-magnetic radiation not entering the cavity may increase themeasurement range of the substance detectable.

Referring back to FIG. 3, and as previously stated, at least someembodiments are configured to increase the amount of substance detected.The measurement range is limited by a number of factors such as thecavity saturation, cavity detector dynamic range and Analog-to-Digitalconverters. The goal of the cavity system is to enhance the substancedetection at very low levels such as 1 to 1000 ppm. In order to extendthe measurement range to higher values the detectors outside the cavitymay be utilized.

The substance absorbs electro-magnetic radiation outside the cavity inthe optical paths of a beam splitter 260 and a reference Substance 262.As shown, for an embodiment, the detectors are arranged in a physicalconfiguration such that the propagation length of the path from the beamsplitter 260 to the normalization detector 261 and the path from theBeam splitter 260 to the reference substance detector 263 is different;therefore the information from the normalization detector 261 andreference substance detector 263 can be used to determine the amount ofthe substance detected by measuring losses external to the cavity.

The cavity 220 improves measurement sensitivity by adding gain to thesystem to measure the substance at very low levels of concentration. Inthe absence of the cavity 220 the substance may be detected at higherlevels of concentration. By combining the information derived from thecavity 220 and cavity detector 230 with information derived outside thecavity through the normalization detector 261 and reference substancedetector 263 the concentration range of substance detected can beextended.

FIG. 16 is a flow chart that includes steps of a method to measure data,according to an embodiment. A first step 1610 includes generating, by atunable light source, a beam of electro-magnetic radiation, wherein awavelength of the beam of electro-magnetic radiation is tuned to operateat a plurality of wavelengths. A second step 1620 includes receiving, byan optical cavity, the beam of electro-magnetic radiation, wherein thephysical characteristics of the optical cavity define a plurality ofallowed axial-plus-transverse electro-magnetic radiation modes, whereinonly a subset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes are excited when the optical cavityreceives the beam of electro-magnetic radiation. A third step 1630includes sensing, by a cavity detector, electro-magnetic radiationemanating from the optical cavity. A fourth step 1640 includesreceiving, by a processor, information relating to the sensedelectro-magnetic radiation. A fifth step 1650 includes detecting thesubstance within the optical cavity based on at least one of anintensity, an amplitude, a phase, or an amplitude and phase of thesensed electro-magnetic radiation emanating from the optical cavity atone or more of the plurality of wavelengths while the optical cavityreceives the beam of electro-magnetic radiation.

As previously described, for at least some embodiments, detecting thesubstance is based on a variation in a shape of an intensity, anamplitude, a phase, or an amplitude and phase of axial-plus-transverseelectromagnetic modes of the sensed electro-magnetic radiation. Aspreviously described, for at least some embodiments, detecting thesubstance comprises summing at least one of an intensity, an amplitude,a phase, or an amplitude and phase of axial-plus-transverseelectromagnetic modes of the sensed electro-magnetic radiation.

As previously described, at least some embodiments include sensing, by anormalization detector, electro-magnetic radiation reflected off anentrance to the optical cavity, wherein the processor further operatesto monitor the sensed electro-magnetic radiation reflected off theentrance to the optical cavity. As previously described, at least someembodiments include accounting for effects of electro-magnetic radiationchanges emanating from the cavity caused by changes in an intensity,amplitude, phase, or amplitude and phase of the electro-magneticradiation entering the cavity comprising measuring the intensity,amplitude, phase, or amplitude and phase of the sensed electro-magneticradiation reflected off the entrance to the optical cavity andcorrecting the electro-magnetic radiation emanating from the cavitybased on the measured intensity.

As previously described, at least some embodiments include tuning thewavelength of the beam of electro-magnetic radiation based on monitoringof a reference electromagnetic radiation exiting from a referencesubstance, wherein at least a portion of the electro-magnetic radiationreflected off the entrance to the optical cavity is passed through thereference substance, and wherein the reference substance is selected toinsure that a frequency of the electro-magnetic radiation corresponds toa frequency at which an absorption of the substance is measured.

As previously described, at least some embodiments include tuning thebeam of electro-magnetic radiation over the plurality of wavelengths oneor multiple times, and recording the sensed electro-magnetic radiationat the plurality of wavelengths. As previously described, at least someembodiments include summing the recorded sensed electro-magneticradiation for each of the plurality of wavelengths over the one ormultiple times. As previously described, at least some embodimentsinclude identifying repetitive patterns in the recorded sensedelectro-magnetic radiation for each of the plurality of wavelengths overthe one or multiple times. As previously described, at least someembodiments include detecting an amount of the substance based on theidentified repetitive patterns in the summed recorded sensedelectro-magnetic radiation for each of the plurality of wavelengths overthe one or multiple times.

As previously described, at least some embodiments include receiving, bythe processor, information from one or more detectors relating to aportion of the beam of electro-magnetic radiation not entering thecavity, wherein information received from the cavity detector andinformation received from one or more detectors are used to detect thesubstance.

Although specific embodiments have been described and illustrated, theembodiments are not to be limited to the specific forms or arrangementsof parts so described and illustrated. The described embodiments are toonly be limited by the claims.

What is claimed:
 1. A system for detecting a substance, comprising: atunable light source wherein the tunable light source generates a beamof electro-magnetic radiation, wherein a wavelength of the beam ofelectro-magnetic radiation is tuned to operate at a plurality ofwavelengths; an optical cavity, wherein the optical cavity receives thebeam of electro-magnetic radiation, wherein physical characteristics ofthe optical cavity define a plurality of allowed axial-plus-transverseelectro-magnetic radiation modes, wherein only a subset of the pluralityof allowed axial-plus-transverse electro-magnetic radiation modes areexcited when the optical cavity receives the beam of electro-magneticradiation; a normalization detector, wherein the normalization detectoris operative to sense electro-magnetic radiation entering the opticalcavity; a processor operating to: receive information relating to thesensed electro-magnetic radiation within or entering the optical cavity;detect the substance at least one of within or outside the opticalcavity based on at least one of an intensity, an amplitude, a phase, oran amplitude and phase of the sensed electro-magnetic radiationemanating from at least one of within or entering the optical cavity atone or more of the plurality of wavelengths while the optical cavityreceives the beam of electro-magnetic radiation; and account for effectsof electro-magnetic radiation changes caused by changes in intensity,amplitude, phase, or amplitude and phase of the electro-magneticradiation entering the cavity comprising measuring intensity, amplitude,phase, or amplitude and phase of the sensed electro-magnetic radiationentering the optical cavity.
 2. The system of claim 1 wherein thenormalization detector is further operative to sense electro-magneticradiation reflected off an entrance to the optical cavity.
 3. The systemof claim 1, wherein the optical cavity comprises a waist size and awaist location, and wherein a waist size or waist location of the beamof electro-magnetic radiation is mode mismatched with at least one ofthe waist size or the waist location of the optical cavity, therebyexciting the subset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes when the optical cavity receives thebeam of electro-magnetic radiation, and wherein the subset includesgreater than one axial-plus-transverse electro-magnetic radiation mode.4. The system of claim 1, wherein the optical cavity comprises an axis,and wherein the beam of electro-magnetic radiation is misaligned withthe axis of the optical cavity, thereby exciting the subset of theplurality of allowed axial-plus-transverse electro-magnetic radiationmodes when the optical cavity receives the beam of electro-magneticradiation, and wherein the subset includes greater than oneaxial-plus-transverse electro-magnetic radiation mode.
 5. The system ofclaim 1, wherein the beam of electro-magnetic radiation comprises morethan one transverse mode , thereby exciting the subset of the pluralityof allowed axial-plus-transverse electro-magnetic radiation modes whenthe optical cavity receives the beam of electro-magnetic radiation, andwherein the subset includes greater than one axial-plus-transverseelectro-magnetic radiation mode.
 6. The system of claim 1, wherein thesubstance is detected based on a variation in a shape of an intensity,an amplitude, a phase, or an amplitude and phase ofaxial-plus-transverse electromagnetic modes of the sensedelectro-magnetic radiation.
 7. The system of claim 1, wherein detectingthe substance comprises summing at least one of an intensity, anamplitude, a phase, or an amplitude and phase of axial-plus-transverseelectromagnetic modes of the sensed electro-magnetic radiation.
 8. Thesystem of claim 1, wherein the processor further operates to tune thewavelength of the beam of electro-magnetic radiation based on monitoringelectromagnetic radiation exiting from a reference substance, wherein atleast a portion of the electro-magnetic radiation reflected off theentrance to the optical cavity is passed through the referencesubstance, and wherein the reference substance is selected to insurethat a frequency of the electro-magnetic radiation corresponds to afrequency at which an absorption of the substance is measured.
 9. Thesystem of claim 1, wherein the processor further operates to: tune thebeam of electro-magnetic radiation over the plurality of wavelengths oneor multiple times; and record the sensed electro-magnetic radiation atthe plurality of wavelengths.
 10. The system of claim 9, wherein theprocessor further operates to: sum the recorded sensed electro-magneticradiation for each of the plurality of wavelengths over the one ormultiple times.
 11. A method of detecting a substance, comprising:generating, by a tunable light source, a beam of electro-magneticradiation, wherein a wavelength of the beam of electro-magneticradiation is tuned to operate at a plurality of wavelengths; receiving,by an optical cavity, the beam of electro-magnetic radiation, whereinphysical characteristics of the optical cavity define a plurality ofallowed axial-plus-transverse electro-magnetic radiation modes, whereinonly a subset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes are excited when the optical cavityreceives the beam of electro-magnetic radiation; sensing, by anormalization detector, electro-magnetic radiation entering the opticalcavity; receiving, by a processor, information relating to the sensedelectro-magnetic radiation within or entering the optical cavity;detecting the substance at least one of within or outside the opticalcavity based on at least one of an intensity, an amplitude, a phase, oran amplitude and phase of the sensed electro-magnetic radiationemanating from a least one of within or entering the optical cavity atone or more of the plurality of wavelengths while the optical cavityreceives the beam of electro-magnetic radiation; and accounting foreffects of electro-magnetic radiation changes caused by changes inintensity, amplitude, phase, or amplitude and phase of theelectro-magnetic radiation entering the cavity comprising measuringintensity, amplitude, phase, or amplitude and phase of the sensedelectro-magnetic radiation entering the optical cavity.
 12. The methodof claim 11, further comprising sensing, by the normalization detector,electro-magnetic radiation reflected off an entrance to the opticalcavity.
 13. The method of claim 11, wherein the optical cavity comprisesa waist size and a waist location, and wherein a waist size or waistlocation of the beam of electro-magnetic radiation is mode mismatchedwith at least one of the waist size or the waist location of the opticalcavity, thereby exciting the subset of the plurality of allowedaxial-plus-transverse electro-magnetic radiation modes when the opticalcavity receives the beam of electro-magnetic radiation, and wherein thesubset includes greater than one axial-plus-transverse electro-magneticradiation mode.
 14. The method of claim 11, wherein the optical cavitycomprises an axis, and wherein the beam of electro-magnetic radiation ismisaligned with the axis of the optical cavity, thereby exciting thesubset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes when the optical cavity receives thebeam of electro-magnetic radiation, and wherein the subset includesgreater than one axial-plus-transverse electro-magnetic radiation mode.15. The method of claim 11, wherein the beam of electro-magneticradiation comprises more than one transverse mode , thereby exciting thesubset of the plurality of allowed axial-plus-transverseelectro-magnetic radiation modes when the optical cavity receives thebeam of electro-magnetic radiation, and wherein the subset includesgreater than one axial-plus-transverse electro-magnetic radiation mode.16. The method of claim 11, wherein the substance is detected based on avariation in a shape of an intensity, an amplitude, a phase, or anamplitude and phase of axial-plus-transverse electromagnetic modes ofthe sensed electro-magnetic radiation.
 17. The method of claim 11,wherein detecting the substance comprises summing at least one of anintensity, an amplitude, a phase, or an amplitude and phase ofaxial-plus-transverse electromagnetic modes of the sensedelectro-magnetic radiation.
 18. The method of claim 11, furthercomprising tuning the wavelength of the beam of electro-magneticradiation based on monitoring electromagnetic radiation exiting from areference substance, wherein at least a portion of the electro-magneticradiation reflected off the entrance to the optical cavity is passedthrough the reference substance, and wherein the reference substance isselected to insure that a frequency of the electro-magnetic radiationcorresponds to a frequency at which an absorption of the substance ismeasured.
 19. The method of claim 11, further comprising: tuning thebeam of electro-magnetic radiation over the plurality of wavelengths oneor multiple times; and recording the sensed electro-magnetic radiationat the plurality of wavelengths.
 20. The method of claim 19, furthercomprising: summing the recorded sensed electro-magnetic radiation foreach of the plurality of wavelengths over the one or multiple times.